Differentiating both sides of eq. (i) w.r.t 
we have
= eq. (ii)
Hence, Function given by eq. (i) is a solution of
verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \[\mathbf{x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{ta}{{\mathbf{n}}^{-\mathbf{1}}}\mathbf{y}\text{ }:\text{ }{{\mathbf{y}}^{\mathbf{2}}}~\mathbf{y}\prime \text{ }+\text{ }{{\mathbf{y}}^{\mathbf{2}}}~+\text{ }\mathbf{1}\text{ }=\text{ }\mathbf{0}\]
verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \[\mathbf{x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{ta}{{\mathbf{n}}^{-\mathbf{1}}}\mathbf{y}\text{ }:\text{ }{{\mathbf{y}}^{\mathbf{2}}}~\mathbf{y}\prime \text{ }+\text{ }{{\mathbf{y}}^{\mathbf{2}}}~+\text{ }\mathbf{1}\text{ }=\text{ }\mathbf{0}\]